Data privacy concerns are increasing significantly in the context of the Internet of Things, cloud services, edge computing, artificial intelligence applications, and other applications enabled by next-generation networks. Homomorphic encryption addresses privacy challenges by enabling multiple operations to be performed on encrypted messages without decryption. This article comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. This article delves into the mathematical foundations required to understand fully homomorphic encryption ($\textsf {FHE}$). It consequently covers design fundamentals and security properties of$\textsf {FHE}$and describes the main$\textsf {FHE}$schemes based on various mathematical problems. On a more practical level, this article presents a view on privacy-preserving machine learning using homomorphic encryption and then surveys$\textsf {FHE}$at length from an engineering angle, covering the potential application of$\textsf {FHE}$in fog computing and cloud computing services. It also provides a comprehensive analysis of existing state-of-the-art$\textsf {FHE}$libraries and tools, implemented in software and hardware, and the performance thereof.

Modular inversion, the multiplicative inverse of an integer in the ring of integers modulo a prime number, is widely used in public-key cryptography. However, it is one of the most computationally intensive operations, thus, it remains the main performance bottleneck for many cryptographic algorithms.This paper presents to the best of the author’s knowledge, the first FPGA-based hardware design for computing the multiplicative inverse using the recently proposed fast constant-time Greatest Common Divisor (GCD) algorithm. This paper introduces two distinct design architectures targeting different applications: (a) a full-width design and (b) a sequential design. The presented designs are compact, parameterizable, and scalable in terms of area and speed. The evaluation shows the proposed designs, which are constant-time and protect against timing-based attacks, outperform existing software and hardware implementations that use other modular inversion techniques. As a specific example, this work presents an evaluation focusing on the use of the multiplicative inverse hardware module to accelerate the ElGamal cryptosystem. The proposed design achieves a speed-up of 90% in the modular inverse calculation and a speed-up of 45% in the overall ElGamal decryption algorithm using our sequential hardware design of fast constant-time GCD algorithm.In addition to developing the fast hardware implementation, this work potentially opens up a new direction for designing cryptosystems: the inverse operation is often avoided when designing algorithms, due to its complexity. With the new hardware module, using the inverse becomes more tractable, making it more appealing to use in the design of new cryptosystems.

Recent works on reducing the size of Error Correcting Codes have investigated the usage of rank metric instead of Hamming metric. Numerous proposals for the NIST Post-Quantum Cryptography competition, including four second round candidates, rely on these codes. In this paper, we discuss several non-trivial issues when porting these schemes into real-world systems on different platforms, such as Intel x86, Armv6 and Armv8. We provide insights on how to implement the underlying finite field and polynomial arithmetic, or the generation of errors of a given rank in constant-time, and report execution time of several rank-based cryptosystems, showing that the achieved performance is similar to those of some of the most popular lattice-based cryptosystems.

It is notably challenging to design an efficient and secure signature scheme based on error-correcting codes. An approach to build such signature schemes is to derive it from an identification protocol through the Fiat-Shamir transform. All such protocols based on codes must be run several rounds, since each run of the protocol allows a cheating probability of either 2/3 or 1/2. The resulting signature size is proportional to the number of rounds, thus making the 1/2 cheating probability version more attractive. We present a signature scheme based on double circulant codes in the rank metric, derived from an identification protocol with cheating probability of 2/3. We reduced this probability to almost 1/2 to obtain the smallest signature among code-based signature schemes based on the Fiat-Shamir paradigm, around 22 KBytes for 128 bit security level. Furthermore, among all code-based signature schemes, our proposal has the lowest value of signature plus public key size, and the smallest secret and public key sizes. We provide a security proof in the Random Oracle Model, implementation performances, and a comparison with the parameters of similar signature schemes.

Data centers being an architectural and functional block of cloud computing are integral to the Information and Communication Technology (ICT) sector. Cloud computing is rigorously utilized by various domains, such as agriculture, nuclear science, smart grids, healthcare, and search engines for research, data storage, and analysis. A Data Center Network (DCN) constitutes the communicational backbone of a data center, ascertaining the performance boundaries for cloud infrastructure. The DCN needs to be robust to failures and uncertainties to deliver the required Quality of Service (QoS) level and satisfy Service Level Agreement (SLA). In this paper, we analyze robustness of the state-of-the-art DCNs. Our major contributions are: (a) we present multi-layered graph modeling of various DCNs; (b) we study the classical robustness metrics considering various failure scenarios to perform a comparative analysis; (c) we present the inadequacy of the classical network robustness metrics to appropriately evaluate the DCN robustness; and (d) we propose new procedures to quantify the DCN robustness. Currently, there is no detailed study available centering the DCN robustness. Therefore, we believe that this study will lay a firm foundation for the future DCN robustness research.